Any urban environment is 9 meals away from anarchy (credit to Kevin Reeve, OnPoint Tactical). After three days with no food, you will find that civil order goes right out the window. People will form groups because a group is more effective. Those groups will take up arms because a group with weapons is more effective. Those groups will take what they want, and they will kill you without thinking twice if they believe that killing you will keep them alive. By the same token, killing them might keep you alive if they're coming for your a) food b) shelter c) family.
Man is not civilized. We have the veneer of culture and civilization, but it is tenuous. Without power you will quickly lose food and sanitation, and after 3 days of that you'll see how civilized man is. The concept is difficult to embrace - we all want our neighbors to be reasonable. We want ourselves to be reasonable. However, if you are unwilling to look at the avenue of anarchy as one of the scenarios for which you should prepare, then you will find yourself unprepared if those whom you hope are civilized in the face of death turn out to be something else.
There are two types of disaster for which one should prepare - short-term (up to two weeks) and long-term (one to six months). Anything longer than six months will likely result in a huge change as you adapt to your new life, so planning to "weather" that disaster type may be more difficult than planning to adapt to it permanently (think post-nuclear, health epidemic, other massive destruction on a global scale). A short-term disaster can be weathered in your home with adequate food, water, and security. There are specific skills you can learn that will make survival in an urban environment easier (again, see OnPoint link above), and if you have to escape the city, those skills are even more valuable. Once outside of the city, wilderness survival skills will be a necessity. A long-term disaster is one where civil order breaks down and your survival becomes paramount. For this you should have plans that include evacuation routes (don't take the freeway or you'll find yourself sitting there days later without fuel in your car), food/supply caches along those routes, and a plan for long-term survival in a location where you will be safe.
It is unfortunate, but those who are not able to protect themselves and their families will likely die. Protect doesn't mean only with weapons in the event of an attack. Protect means "find food when your local grocery is empty." Protect means "find shelter that will keep us warm in winter if there is no heating oil." Protect means "understand basic medical treatment" and "maintain calm in a situation of terrible stress." If you have not prepared for a disaster, then when the disaster strikes, what's your plan? To go to the shelter and wait for the government? Those in New Orleans who went to the Superdome found themselves the victims of gangs of thugs and rapists demanding payments for using the toilets. I'll leave discussion of the type of payments accepted as an exercise for the reader.
Japan is an interesting case because civil order has been maintained. I don't know the reason behind this - maybe it's cultural. Maybe it's the respect they have for one another. Maybe it's because there is no food for anyone to take because everything was wiped out. People are leaving the areas of destruction and going to other cities where they have family, so perhaps the local suffering is manageable. Japan's disaster response from the government also appears to have been well-executed. This post-disaster stability is the exception. It is not the norm. If your community handles its disasters with the same calm, then you are fortunate.
Unless you plan to not be a victim, then you will find yourself exactly where you planned to be.
To answer the OP's question, I currently live in Kraków, Poland and go back and forth between Kraków and New York. My wife and I have 30 days of non-perishable food and bottled water in our home and the ability to create fire and cook using small amounts of various fuel types (alcohol penny stoves and two large rocket stoves made from 5L Heineken kegs). I have a Toyota Land Cruiser that runs on diesel fuel, and this summer we'll be preparing remote caches for supplies outside of the city in the event we have to leave. We have camping supplies (tent, sleeping bags, knives, machete, axe, 2-way radios, etc). Gun control in Poland makes it difficult to get a handgun or rifle/shotgun, but if I could, I would get a 12-gauge shotgun because of its versatility for both hunting and defense. We both have training in urban survival and I have training in wilderness survival. We're both trained in Krav Maga. Our caches will contain hard and soft copies of important documents and data (passports, identity cards, marriage license, birth certificates, etc), some money, and additional supplies. For the business we have copies of all of our data and documents in a massive fire safe. For short-term disasters this is fine. For a long-term disaster this should also be fine. Honestly, if I have to survive six months outside of the city, something bad happened. I may not go back to working in IT or even using computers for a long time.
This year we're going to be moving back to the US, and we talked about if it made sense to move back to New York (I own businesses in NYC and in Kraków). We decided that we'll be moving to Colorado instead, and the decision was largely based on the need for flexibility. In Colorado we have the same ability as we do here to weather a disaster in the city or move outside of the city to a safer area. In Colorado it's also easier to purchase firearms than it is in NYC.
I don't believe that I'm any sort of survival nut or apocalypse junkie. I'm not worried about the Chinese or the Terrorists - I'm more worried about the US government screwing its people than anyone screwing the US. However, I do believe very strongly in being prepared and in being flexible. My approach here is the same as my approach to firearms training: despite how you feel about firearms, if you ever have to shoot a gun, it's a very bad time to learn. Hope for the best. Prepare for the worst.